Kth Largest Element in an Array (QuickSelect)

Find the Kth largest element in an unsorted array in O(N) average time.

Sort Colors (Dutch National Flag Partitioning)

Sort an array of 0s, 1s, and 2s in a single pass using three pointers.

Avoid O(N²) Worst-Case in QuickSort

Discuss strategies to prevent quadratic runtime on already sorted or duplicate-heavy inputs.

Searching & Sorting AlgorithmsIntermediate LevelStudy Time: 25 mins

Quick Sort Algorithm

Quick Sort is a Divide and Conquer algorithm that selects a pivot element, partitions the array around the pivot, and recursively sorts the sub-arrays.

Quick Sort Visualizer

Array loaded. Trigger Quick Sort to visualize partitioning.

35

[0]

15

[1]

55

[2]

45

[3]

25

[4]

65

[5]

Speed:

Real-world analogy: Height Line Sorting

Pivot

Hover over items for details

Pick a person as pivot. Everyone shorter moves to the left, everyone taller moves to the right. Repeat recursively for left and right groups.

Pivot= Element chosen to partition the dataset into left/right subsets.

Complexity analysis

Scenario Simulator: Dataset Size (N = 500)

Presets:

N = 10N = 10,000

Complexity Curve MapQuick Sort: O(N log N) Linearithmic Time

Hover curves to inspect classes

Time Steps (N=500)

~4,483 steps (Linearithmic)

O(N log N) Linearithmic Time

Space Footprint

O(log N) Stack

Memory growth rate as N expands.

Performance Rank

Moderate Tier

Relative efficiency rating for large N.

Operation	Time Complexity	Space Complexity
Best / Average Case	O(N log N)	O(log N)
Worst Case (Sorted Array w/ bad pivot)	O(N²)	O(N)

Code implementations

function quickSort(arr, low = 0, high = arr.length - 1) {
  if (low < high) {
    const pi = partition(arr, low, high);
    quickSort(arr, low, pi - 1);
    quickSort(arr, pi + 1, high);
  }
  return arr;
}